A note on the metastability in three modifications of the standard Ising model

TL;DR

This paper extends previous studies on metastability in three variants of the 2D Ising model, applying potential-theoretic methods to derive more precise asymptotic transition times at low temperature.

Contribution

It introduces a potential-theoretic approach to analyze metastability in anisotropic, next-nearest-neighbor, and alternating field Ising models, refining earlier pathwise results.

Findings

More precise asymptotic estimates of transition times

Extension of metastability analysis to new Ising model variants

Application of potential-theoretic methods to low-temperature dynamics

Abstract

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model is an anisotropic version, where the interaction energy takes different values on vertical and on horizontal bonds. The second model adds next-nearest-neighbor attraction to the standard Ising model. And the third model associates different alternating signs for the magnetic fields on even and odd rows. All these models have already been studied, and results concerning metastability have been established using the so-called pathwise approach. In this text, we extend these earlier results, and apply the potential-theoretic approach to metastability to obtain more precise asymptotic information on the transition time from the metastable phase to the stable phase.